论文标题
解决方案的定性属性，用于共同不变的第四阶关键系统
Qualitative properties for solutions to conformally invariant fourth order critical systems
论文作者
论文摘要
我们研究了非负解决方案的定性特性，用于涉及关键指数的第四阶方程的共形耦合系统。对于在刺穿空间中定义的解决方案，基本上存在两种案例可以分析。如果原点是可移动的奇异性，我们证明非单明的溶液是旋转不变的，并且弱积极。更确切地说，它们是单位矢量具有非负坐标的第四阶球形溶液的产物。如果原点是不可易换的奇异性，我们表明溶液在径向对称且强烈正面。此外，使用pohozaev型不变性，我们证明了半单打溶液的不存在，也就是说，所有组件在原产地附近同样爆炸。也就是说，它们被归类为Emden的倍数 - FOWLER解决方案。我们的结果是由于[L. A. Caffarelli，B。Gidas和J. Spruck，Comm。纯应用。数学。 （1989）]在经典的Yamabe方程式上。
We study qualitative properties for nonnegative solutions to a conformally invariant coupled system of fourth order equations involving critical exponents. For solutions defined in the punctured space, there exist essentially two cases to analyze. If the origin is a removable singularity, we prove that non-singular solutions are rotationally invariant and weakly positive. More precisely, they are the product of a fourth order spherical solution by a unit vector with nonnegative coordinates. If the origin is a non-removable singularity, we show that the solutions are radially symmetric and strongly positive. Furthermore, using a Pohozaev-type invariant, we prove the non-existence of semi-singular solutions, that is, all components equally blow-up in the neighborhood of origin. Namely, they are classified as multiples of the Emden--Fowler solution. Our results are natural generalizations of the famous classification due to [L. A. Caffarelli, B. Gidas and J. Spruck, Comm. Pure Appl. Math. (1989)] on the classical singular Yamabe equation.
